The “Story Teller” fight scene: In my mind, this is strongest form of fight scene writing, and it's been used by many recent successful novels. This form is all about the writing style of the author and the authenticity of the viewpoint character, meaning that for the technique to work, the writer must capture the personality of the viewpoint character perfectly.
Example: The Blade Itself (2006) by Joe Abercrombie
It wasn’t ’til the Dogman was hid behind a bush with his bow in his hand and a shaft at the ready that he realised. He’d no idea what the signal was. He looked down at the Shanka, still sat there all unwary, grunting and shouting and banging about. By the dead he needed to piss. Always needed to piss before a fight. Had anyone said the signal? He couldn’t remember.
“Shit,” he whispered, and just then Dow came hurtling out from the trees, axe in one hand, sword in the other.
“Fucking Flatheads!” he screamed, giving the nearest a fearsome big blow in the head and splattering blood across the clearing. In so far as you could tell what a Shanka was thinking, these ones looked greatly surprised. Dogman reckoned that would have to do for a signal.
He let loose his shaft at the nearest Flathead, just reaching for a big club and watched it catch it through the armpit with a satisfying thunk. “Hah!” he shouted. He saw Dow spit another through the back with his sword, but there was a big Shanka now with a spear ready to throw. An arrow came looping out of the trees and stuck it through the neck, and it let go a squeal and sprawled out backwards. That Grim was a damn good shot.
Now Threetrees came roaring from the scrub on the other side of the clearing, catching them off guard. He barged one Flathead in the back with his shield and it sprawled face-first into the fire, he hacked at another with his sword. The Dogman let go a shaft and it stuck a Shanka in its gut. It dropped down on its knees and a moment later Tul took its head off with a great swing of his sword.
The fight was joined and moving quick—chop, grunt, scrape, rattle. There was blood flying and weapons swinging and bodies dropping too fast for the Dogman to try an arrow at. The three of them had the last few hemmed in, squawking and gibbering. Tul Duru was swinging his big sword around, keeping them at bay. Threetrees darted in and chopped the legs out from under one, and Dow cut another down as it looked round.
The last one squawked and made a run for the trees. Dogman shot at it, but he was hurrying and he missed. The arrow almost hit Dow in the leg, but luckily he didn’t notice. It had almost got away into the bushes, then it squealed and fell back, thrashing. Forley had stabbed it, hiding in the scrub. “I got one!” he yelled.
What makes it work:
Abercrombie has a gift for creating vivid, unique characters, each with a powerful voice. In the example above, the protagonist is a lowborn, somewhat wild, Northman who has spent his whole life fighting. The reader can almost ascertain all of this just from the voice of the character, and the rhythm and flow feel as if a great storyteller is telling the story in a hall or at a campfire.
There is also a “grittiness” to the fight above, and to most of Abercrombie’s fight scenes, but Abercrombie does change the style enough from character to character to keep the feelings and descriptions authentic to the POV characters.
Why it doesn’t always work:
Not all writers are great “storytellers.” When the writer fails to capture the voice of the character well, the fighting becomes distant and feels like the author is telling the reader about the fight third hand (as in the dreaded workshop words: you are telling vs. showing).
There are a lot of action verbs. Keeping these verbs in the tone of the viewpoint character is vital to maintaining excitement and tension, keeping the description authentic to the character, and moving the scene along at a rolling, fast pace.